Abstract
The best linear unbiased predictor (BLUP) is called a kriging predictor and has been widely used to interpolate a spatially correlated random process in scientific areas such as geostatistics. However, if an underlying random field is not Gaussian, the optimality of the BLUP in the mean squared error (MSE) sense is unclear because it is not always identical with the conditional expectation. Moreover, in many cases, data sets in spatial problems are often so large that a kriging predictor is impractically time-consuming. To reduce the computational complexity, covariance tapering has been developed for large spatial data sets. In this paper, we consider covariance tapering in a class of transformed Gaussian models for random fields and show that the BLUP using covariance tapering, the BLUP and the optimal predictor are asymptotically equivalent in the MSE sense if the underlying Gaussian random field has the Matérn covariance function.
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Acknowledgments
The authors are grateful to Professor Akimichi Takemura and Professor Mark G. Genton for helpful comments and discussions. We also acknowledge the suggestions from the associate editor and three anonymous referees that refined and improved the manuscript. This work is supported by the Research Fellowship (DC1) from the Japan Society for the Promotion of Science and by the Grants-in-Aid for Scientific Research (A) 23243039 from the Japanese Ministry of Education, Science, Sports, Culture and Technology.
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Hirano, T., Yajima, Y. Covariance tapering for prediction of large spatial data sets in transformed random fields. Ann Inst Stat Math 65, 913–939 (2013). https://doi.org/10.1007/s10463-013-0399-8
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DOI: https://doi.org/10.1007/s10463-013-0399-8